An independent home builder’s annual profit, in thousands of dollars, can be modeled by the function P(x)=5.152x^3 – 143x^2 + 1102x – 1673, where x is the number of houses built in a year. His company can build at most 13 houses in a year. Find the y and x intercepts and explain what they mean in this context. Determine the domain of the function in the context of this problem as well. How many hours should the builder construct in order to have a profit of at least $400,000? How many houses should the builder construct in order to maximize profit?